Abstract
Abstract. This paper presents a heuristic building block for wind farm layout optimization algorithms. For each pair of wake-interacting turbines, a vector is defined. Its magnitude is proportional to the wind speed deficit of the waked turbine due to the waking turbine. Its direction is chosen from the inter-turbine, downwind, or crosswind directions. These vectors can be combined for all waking or waked turbines and averaged over the wind resource to obtain a vector, a “pseudo-gradient”, that can take the role of gradient in classical gradient-following optimization algorithms. A proof-of-concept optimization algorithm demonstrates how such vectors can be used for computationally efficient wind farm layout optimization. Results for various sites, both idealized and realistic, illustrate the types of layout generated by the proof-of-concept algorithm. These results provide a basis for a discussion of the heuristic's strong points – speed, competitive reduction in wake losses, and flexibility – and weak points – partial blindness to the objective and dependence on the starting layout. The computational speed of pseudo-gradient-based optimization is an enabler for analyses that would otherwise be computationally impractical. Pseudo-gradient-based optimization has already been used by industry in the design of large-scale (offshore) wind farms.
Highlights
IntroductionIts layout is one of the most important design choices a developer has to make
For any wind farm, its layout is one of the most important design choices a developer has to make
We present a new heuristic optimization algorithm that uses some of the steps of the cost function – most notably the energy losses per wind direction sector – to construct a so-called pseudo-gradient
Summary
Its layout is one of the most important design choices a developer has to make. A layout optimization for a large (offshore) wind farm – which could involve tens to hundreds of turbines to be placed in a possibly very complex polygon – is demanding in terms of computational power since it requires a wake model run for every cost function evaluation. A formal gradient-based optimization uses the objective function’s gradient, which is the vector of partial derivatives of this function with respect to the design variables. The (negative) gradient at a given design variable vector corresponds to the direction of steepest ascent (descent) of the objective and has a magnitude reflecting the steepness. The optimizer would follow the negative gradient in a stepwise fashion over design variable vectors corresponding to decreasing objective function value. Pseudo-gradients are in practice defined for design variable components corresponding to a single turbine. Pseudo-gradients can be visualized as vectors attached to individual turbines in the design space
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